John Munson/The Star-LedgerYankees reliever Damaso Marte (left shoulder) thought he might be out of baseball.

NEW YORK — Of the two Yankees who showed up to clean out their lockers this afternoon at Yankee Stadium, one’s condition will have a direct effect on the other’s offseason.

Damaso Marte strolled in first, his left arm in a navy blue sling just two days after surgery on a shoulder injury that ended his season in early July.

The left-handed specialist, a stalwart during the Yankees’ 2009 World Series run, had thought his career was finished. But in talking to his doctors Marte discovered that things might not be as grim as he first thought.

The team of doctors in Cincinnati, where the surgery was performed, told Marte that he should be able to start throwing again after next season’s All-Star break.

“I thought maybe I wouldn’t throw anymore,” said Marte, who is set to make $4 million next year with an option for 2012. “It was a lot of pain. Right now I feel comfortable because my doctor, he gave me a good idea with my arm and he told me it’s getting better.”

Boone Logan, the man who took Marte’s place as the left-hander in the bullpen, arrived in the clubhouse a few minutes later. After going 2-0 with a 2.93 ERA in 51 appearances during the regular season, Logan said he’s approaching the offseason with the expectation that he’ll be the team’s go-to left-handed specialist next season.

He said he’ll work on keeping his arm motion familiar during his downtime so he can jump straight into workouts.

“I might try to keep my arm motion going in the offseason just so it doesn’t take that long to get into shape,” Logan said. “Last year was the first year I kept my arm motion going. It made it easier in the spring. It’s kind of what I want to do again next year, take the same approach.”